7 problems

Let $T_{p,q}$ be a torus knot with parameters $p$ and $q$. Milnor's conjecture. The smooth 4-genus of $T_{p,q}$ is … The conjecture is a theorem, proved by Kronheimer and Mrowka, a…

The Ozsváth–Szabó invariant $\tau$ and Rasmussen invariant $s$ are knot concordance invariants. For integers $p,q$ and $t$, let $D_+(T_{p,q},t)$ denote the $t$-twisted positive dou…

Let $K$ be a knot, and let $W_0(K)$ denote its zero-twisted Whitehead double. Smooth-sliceness conjecture for zero-twisted Whitehead doubles. The knot $K$ is smoothly slice if and…

Let $K$ be a knot, and let $D_1$ and $D_2$ be slice disks for $K$ in $B^4$. Their positive Whitehead doubles are the slice disks obtained by applying the positive Whitehead satelli…

A knot in $S^3$ is slice if it bounds a smoothly embedded disc in $B^4$, and it is ribbon if it bounds a disc in $B^4$ with no local maxima for the radial function. Slice–ribbon co…

Let $M$ be a smooth $4$-manifold with Spin$^c$ structure $\mathfrak{s}$, let $N$ be a smooth $4$-manifold with a finite cyclic group action, and let $\bar{M}_k$ and…

A knot in the 3-sphere is slice if it is concordant to the unknot, equivalently if it bounds a smooth properly embedded disk in the 4-ball. For a knot $K$, let $D(K)$ denote its (p…